The invention relates to the display of piloting assistance information in the cockpit of an aircraft. Modern aircraft, in particular transport aircraft, generally include a system for display of piloting assistance information in their cockpit. A system of this kind, for example of the CDS (Control and Display System) type, controls the display of information on screens, termed head-down screens, in the cockpit: to view this information the user, generally a pilot or copilot of the aircraft, must lower their head to look at the screens. They are therefore not able to see, at the same time, the environment of the aircraft through a windshield of the cockpit. To enable the user to see this information at the same time as monitoring the environment of the aircraft, some aircraft are now equipped with a head-up display (HUD) device. An HUD device includes a projector and a semi-reflecting window (known as a “combiner”) disposed between the windshield of the aircraft and a position corresponding to the position of the head of a pilot or copilot when the latter is in the cockpit to pilot the aircraft. The projector projects information onto the semi-reflecting window and the user can therefore view this information superimposed on the environment of the aircraft visible through the windshield. Some information can be displayed in a conforming manner. In the remainder of the description, the expression in a conforming manner refers to the display of information or a symbol on a display or a transparent screen in such a way that this information or this symbol can be seen by the user superimposed on the external environment of the aircraft, at a position conforming to the meaning of the information or symbol. For example, when it is displayed in a conforming manner, a symbol representing a runway is displayed superimposed on the position of the real runway that the user can see through the windshield of the aircraft. An HUD device of this kind is generally of high cost. Moreover, installing it in an aircraft can be complicated and costly, especially if such installation was not planned during the design of the aircraft. Moreover, the HUD device is not visible to the user, or only partly visible, if the user is called upon to turn their head to monitor the lateral environment of the aircraft: the information displayed on the HUD is then not visible, or only partly visible, to the user.